Tuesday, January 3, 2017

The future is uncertain

Aristotle formulated the openness of the future in the language of logic. Living in Athens at a time when invasion from the sea was always a possibility, he made his argument using the following sentence: ‘There will be a sea-battle tomorrow.’ One of the classical laws of logic is the ‘law of the excluded middle’ which states that every sentence is either true or false: either the sentence is true or its negation is true. But Aristotle argued that neither ‘There will be a sea-battle tomorrow’ nor ‘There will not be a sea-battle tomorrow’ is definitely true, for both possibilities lead to fatalism; if the first statement is true, for example, there would be nothing anybody could do to avert the sea-battle. Therefore, these statements belong to a third logical category, neither true nor false. In modern times, this conclusion has been realised in the development of many-valued logic. ...

Aristotle formulated the openness of the future in the language of logic. Living in Athens at a time when invasion from the sea was always a possibility, he made his argument using the following sentence: ‘There will be a sea-battle tomorrow.’ One of the classical laws of logic is the ‘law of the excluded middle’ which states that every sentence is either true or false: either the sentence is true or its negation is true. But Aristotle argued that neither ‘There will be a sea-battle tomorrow’ nor ‘There will not be a sea-battle tomorrow’ is definitely true, for both possibilities lead to fatalism; if the first statement is true, for example, there would be nothing anybody could do to avert the sea-battle. Therefore, these statements belong to a third logical category, neither true nor false. In modern times, this conclusion has been realised in the development of many-valued logic. ...

Knowledge of the future, therefore, is limited in a fundamental way. It is not that there are true facts about the future, but the knowledge of them is not accessible to us; there are no facts out there, and there is simply no certain knowledge to be had. Nevertheless, there are facts about the future with partial degrees of truth. We can attain knowledge of the future, but that knowledge will always be uncertain.

His explanation is sensible enuf, but it is funny how he has to dive into quantum mechanics to reach the same conclusions that Aristotle reached 2.5 millennia earlier.

Yes, Laplace mentioned a deterministic fantasy in 1814, but he also had a very probabilistic view of the world.